ABSTRACT A simulated annealing approach to the assignment of program tasks to processors in a distributed computer system is presented. Tasks of a program require certain capacitated computer resources. They also communicate at a given rate. Processors are interconnected by a communication network constituted of various types of links: local area network (LAN), wide area network (WAN) and specialised links. The communication resources are also capacitated. The purpose is to find the assignment of tasks to processors such that a measure of performance is optimised, the requirements of each task are met and the capacities of the resources are not violated. Various versions of the problem are identified and formulated. The design of the simulated annealing algorithm to solve the most general version is then described. The results of computational experience are reported